I'll try to answer your question now.
Z = V/I, it is required that in general, V or I or both are also complex.
Keep in mind, that impedance in general, Z, is complex. And so according to the equation:Zoc = V/I
similarly, Zsc = V/I
then Characteristic impedance, Zc = sqrt(Zoc*Zsc)
How can you get phase angle with this???
Z = V/I, it is required that in general, V or I or both are also complex.